the volume of a microbial culture is observed to increase according to the formu

Question

the volume of a microbial culture is observed to increase according to the formula V(cm^3) = e^t where t is time in seconds
a) calculate the expression for V(in^3) in terms of t(h)
b) both the exponential function and its argument must be dimensionless. the given equation seems to violate both of these rules, and yet the equation is valid. explain this paradox. [hint: observe the result of part a]

Explanation / Answer

a. V(cm^3)/0.061 cm^3 = e^(t(h)/3600 h) => 16.39 V(in^3)/in^3 = e^(t(h)/3600 h) b. By dividing by the units we have made the fraction dimensionless both in the power of 'e' and in Volume also. hence satisfied the law.

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